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Gradient Projection for Linearly Constrained Convex Optimization in Sparse Signal Recovery

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Abstract

The $\ell_2$-$\ell_1$ compressed sensing minimization problem can be solved efficiently by gradient projection. In imaging applications, the signal of interest corresponds to nonnegative pixel intensities; thus, with additional nonnegativity constraints on the reconstruction, the resulting constrained minimization problem becomes more challenging to solve. In this paper, we propose a gradient projection approach for sparse signal recovery where the reconstruction is subject to nonnegativity constraints. Numerical results are presented to demonstrate the effectiveness of this approach.

Citation

Z. T. Harmany, D. O. Thompson, R. M. Willett and R. F. Marcia, “Gradient projection for linearly constrained convex optimization in sparse signal recovery”, in IEEE International Conference on Image Processing (ICIP), 2010, 3361–3364.

BibTeX

@inproceedings{harmany-icip2010-lcgp,
  doi = {10.1109/ICIP.2010.5652815},
  title = {Gradient projection for linearly constrained convex optimization in sparse signal recovery},
  author = {Harmany, Zachary T. and Thompson, Daniel O. and Willett, Rebecca M. and Marcia, Roummel F.},
  booktitle = {IEEE International Conference on Image Processing (ICIP)},
  month = {sep},
  year = {2010},
  pages = {3361–3364},
  abstract = {The $\ell_2$-$\ell_1$ compressed sensing minimization problem can be solved efficiently by gradient projection. In imaging applications, the signal of interest corresponds to nonnegative pixel intensities; thus, with additional nonnegativity constraints on the reconstruction, the resulting constrained minimization problem becomes more challenging to solve. In this paper, we propose a gradient projection approach for sparse signal recovery where the reconstruction is subject to nonnegativity constraints. Numerical results are presented to demonstrate the effectiveness of this approach.}
}